- Abstract:
-
Many interesting concepts in mathematics are essentially "cross-domain" in nature, relating objects from more than one area of mathematics, e.g. prime order groups. These concepts are often vital to the formation of a mathematical theory. Often, the introduction of cross-domain concepts to an investigation seems to exercise a mathematician's creative ability. The HR program, (Colton, 1999), proposes new concepts in mathematics. Its original implementation was limited to working in one mathematical domain at a time, so it was unable to create cross-domain concepts. Here, we describe an extension of HR to multiple domains. Cross-domain concept formation is facilitated by generalisation of the data structures and heuristic measures employed by the program, and the implementation of a new production rule. Results achieved include generation of the concepts of prime order groups, graph nodes of maximal degree and an interesting class of graph.
- Copyright:
- 2000 by The University of Edinburgh. All Rights Reserved
- Links To Paper
- No links available
- Bibtex format
- @InProceedings{EDI-INF-RR-0019,
- author = {
Graham Steel
and Simon Colton
and Alan Bundy
and Toby Walsh
},
- title = {Cross Domain Mathematical Concept Formation},
- book title = {Procs of AISB'00 Symposium on Creative and Cultural Aspects of AI and Cognitive Science},
- year = 2000,
- month = {May},
- }
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